Wendelin Werner: Catalogue data in Spring Semester 2019 |  |
| Name | Dr. Wendelin Werner |
| URL | http://www.math.ethz.ch/~wewerner |
| Department | Mathematics |
| Relationship | Full Professor |
| Number | Title | ECTS | Hours | Lecturers | |
|---|---|---|---|---|---|
| 401-3600-19L | Student Seminar in Probability Theory:  Limited number of participants. Registration to the seminar will only be effective once confirmed by email from the organizers. | 4 credits | 2S | A.‑S. Sznitman, J. Bertoin, V. Tassion, W. Werner | |
| Abstract | Selected topics from Probability Theory will be discussed. | ||||
| Learning objective | The seminar is a natural complement to the material discussed in the lecture on probability theory in the 5th semester. | ||||
| Content | The seminar is centered around a topic in probability theory which changes each semester. Example of topics are random walks and electric networks, Markov chains, stochastic integrals, coupling methods, etc. | ||||
| Prerequisites / Notice | There is only a limited number of slots available for this seminar. Participation will only be effective once confirmed by the organizers. | ||||
| 401-3642-00L | Brownian Motion and Stochastic Calculus  | 10 credits | 4V + 1U | W. Werner | |
| Abstract | This course covers some basic objects of stochastic analysis. In particular, the following topics are discussed: construction and properties of Brownian motion, stochastic integration, Ito's formula and applications, stochastic differential equations and connection with partial differential equations. | ||||
| Learning objective | This course covers some basic objects of stochastic analysis. In particular, the following topics are discussed: construction and properties of Brownian motion, stochastic integration, Ito's formula and applications, stochastic differential equations and connection with partial differential equations. | ||||
| Lecture notes | Lecture notes will be distributed in class. | ||||
| Literature | - J.-F. Le Gall, Brownian Motion, Martingales, and Stochastic Calculus, Springer (2016). - I. Karatzas, S. Shreve, Brownian Motion and Stochastic Calculus, Springer (1991). - D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer (2005). - L.C.G. Rogers, D. Williams, Diffusions, Markov Processes and Martingales, vol. 1 and 2, Cambridge University Press (2000). - D.W. Stroock, S.R.S. Varadhan, Multidimensional Diffusion Processes, Springer (2006). | ||||
| Prerequisites / Notice | Familiarity with measure-theoretic probability as in the standard D-MATH course "Probability Theory" will be assumed. Textbook accounts can be found for example in - J. Jacod, P. Protter, Probability Essentials, Springer (2004). - R. Durrett, Probability: Theory and Examples, Cambridge University Press (2010). | ||||
| 401-5600-00L | Seminar on Stochastic Processes | 0 credits | 1K | J. Bertoin, A. Nikeghbali, B. D. Schlein, A.‑S. Sznitman, V. Tassion, W. Werner | |
| Abstract | Research colloquium | ||||
| Learning objective | |||||